The following line passes through point $(10, -8)$ : $y = -\dfrac{1}{2} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(10, -8)$ into the equation gives: $-8 = -\dfrac{1}{2} \cdot 10 + b$ $-8 = -5 + b$ $b = -8 + 5$ $b = -3$ Plugging in $-3$ for $b$, we get $y = -\dfrac{1}{2} x - 3$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(10, -8)$